The main reason I don't see Strength as a dump stat is the buzz I've heard around special melee actions. (Trip, knock down, disarm) which are all Str based. Common scenario I hear is if you do str 1 or 2, prepared to have your weapon ceremoniously ripped from your hands or fall flat on your back.
Main problem I see with this is that it further buffs unarmed, where strength affects DV AND adds to ability to use things like Grapple, Disarm, etc. Becomes really hard to think of a scenario you'd want melee weapon other than your fist.....other than potentially reach? Haven't looked at the range of some of the melee weapons, but if they can go into the next range, instead of just the closest, could see a use there....